The Lattice Bhurw11
An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, RWTH Aachen University
(nebe@math.rwth-aachen.de)
and
Neil J. A. Sloane
(njasloane@gmail.com)
Last modified Fri Jul 18 13:11:00 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME (required)
DIMENSION (required)
GRAM (floating point or integer Gram matrix)
DIVISORS (elementary divisors)
MINIMAL_NORM
PROPERTIES
REFERENCES
NOTES
LAST_LINE (required)
-
NAME (required)
Bhurw11
-
DIMENSION (required)
44
-
GRAM (floating point or integer Gram matrix)
44
6 -1 0 -1 3 1 1 -2 -1 0 1 -3 0 1 -3 1 0 -1 -1 0 0 -1 -2 -1 0 1 1 1 1 -1 1 3 -3 1 2 1 0 0 1 1 0 3 1 0
-1 6 1 1 -2 1 1 1 -2 -1 -1 2 -1 2 0 -1 0 0 1 1 0 -1 -1 2 -1 -1 0 0 -1 0 -1 1 1 1 1 1 -1 0 0 1 -3 0 0 1
0 1 6 0 0 2 -1 2 0 0 -2 1 -3 1 -1 -1 -1 0 1 -1 1 -2 1 1 0 0 0 -1 -1 1 -1 0 1 0 1 -2 -2 -1 -1 0 -1 0 -1 0
-1 1 0 6 -2 2 -1 2 0 -1 0 1 -1 1 0 -1 1 -1 1 -1 -1 0 1 2 -2 0 2 -1 2 0 2 1 0 1 2 -2 0 -1 0 1 0 -1 1 1
3 -2 0 -2 6 -1 0 -1 1 2 1 -3 -1 0 -3 0 -3 1 -2 0 0 -1 -1 -1 2 1 1 1 0 -2 2 2 -1 -2 0 1 3 -1 2 -2 -1 3 -1 -4
1 1 2 2 -1 6 -2 2 0 -1 0 0 -3 3 -2 -1 1 1 1 -2 0 0 1 1 -2 0 2 -1 2 -1 3 3 -3 1 4 -2 0 0 0 2 0 -2 3 2
1 1 -1 -1 0 -2 6 -1 -2 -1 0 1 1 -1 0 1 0 -1 -1 2 1 0 -3 1 0 0 -2 0 -1 -1 -1 0 1 0 -1 3 0 0 -1 0 0 1 -1 1
-2 1 2 2 -1 2 -1 6 1 -1 1 1 -1 1 0 -3 0 0 3 -2 0 0 1 2 -2 1 1 -2 0 2 2 -1 1 -1 1 -1 1 0 -1 2 0 -1 1 1
-1 -2 0 0 1 0 -2 1 6 -1 0 -2 1 -3 2 0 1 0 0 0 -2 2 2 -2 1 0 -1 -1 0 2 0 -1 2 1 -2 -2 2 0 -3 0 3 -2 -1 -1
0 -1 0 -1 2 -1 -1 -1 -1 6 0 -1 -1 0 -2 1 -2 1 -1 -2 1 -1 0 0 1 0 -1 0 0 -3 1 -1 -1 -2 0 0 -1 0 2 -3 -1 2 -2 -3
1 -1 -2 0 1 0 0 1 0 0 6 -1 2 0 1 -2 0 1 0 -1 -1 2 -2 0 -1 0 0 1 1 -1 2 1 -1 -1 1 2 0 2 1 2 0 -1 2 3
-3 2 1 1 -3 0 1 1 -2 -1 -1 6 -1 1 2 0 1 1 0 2 0 -2 0 2 0 1 0 0 0 0 -1 0 2 0 -1 0 -1 -1 0 -1 -1 -1 -1 1
0 -1 -3 -1 -1 -3 1 -1 1 -1 2 -1 6 -3 3 1 2 -1 1 2 -2 3 0 -2 1 0 -2 1 0 1 -2 -2 2 2 -3 1 0 2 -3 1 1 0 0 2
1 2 1 1 0 3 -1 1 -3 0 0 1 -3 6 -3 -2 -1 2 0 -2 2 -3 -1 1 -1 2 2 0 0 -2 3 3 -3 -3 3 1 0 -2 3 1 -3 0 3 0
-3 0 -1 0 -3 -2 0 0 2 -2 1 2 3 -3 6 0 3 0 0 2 -2 2 0 -1 0 -1 -2 1 -1 2 -3 -2 3 2 -3 0 -2 2 -3 0 2 -3 -2 3
1 -1 -1 -1 0 -1 1 -3 0 1 -2 0 1 -2 0 6 0 -2 0 2 -1 1 0 -1 2 0 -1 0 1 0 -2 0 0 3 -1 0 0 0 -1 -1 0 2 -3 -2
0 0 -1 1 -3 1 0 0 1 -2 0 1 2 -1 3 0 6 0 0 1 -1 1 0 -1 -1 0 -1 0 1 1 -1 0 0 3 -1 -1 -2 2 -3 1 2 -2 0 3
-1 0 0 -1 1 1 -1 0 0 1 1 1 -1 2 0 -2 0 6 -2 0 0 -1 0 0 1 1 0 1 0 -3 2 1 0 -3 0 0 1 0 1 -2 -1 -2 1 0
-1 1 1 1 -2 1 -1 3 0 -1 0 0 1 0 0 0 0 -2 6 -2 -1 1 2 1 -2 0 1 -2 1 2 0 -2 0 1 1 -2 0 0 -1 3 0 0 1 2
0 1 -1 -1 0 -2 2 -2 0 -2 -1 2 2 -2 2 2 1 0 -2 6 -2 0 -1 0 2 -1 0 2 0 1 -3 1 3 3 -2 1 1 1 -2 -1 -1 1 -2 -1
0 0 1 -1 0 0 1 0 -2 1 -1 0 -2 2 -2 -1 -1 0 -1 -2 6 -2 -2 0 1 1 -1 0 -2 0 0 0 -2 -3 -1 1 -1 0 1 0 -1 -1 0 -1
-1 -1 -2 0 -1 0 0 0 2 -1 2 -2 3 -3 2 1 1 -1 1 0 -2 6 1 -1 0 -2 -2 -1 0 1 -1 -1 1 3 0 0 0 2 -2 2 2 -2 1 2
-2 -1 1 1 -1 1 -3 1 2 0 -2 0 0 -1 0 0 0 0 2 -1 -2 1 6 -1 0 0 1 -1 1 1 0 -2 1 1 0 -4 1 -1 -1 -1 1 0 1 0
-1 2 1 2 -1 1 1 2 -2 0 0 2 -2 1 -1 -1 -1 0 1 0 0 -1 -1 6 -2 0 1 -1 0 -1 0 1 1 -1 2 0 1 0 2 1 -1 0 0 0
0 -1 0 -2 2 -2 0 -2 1 1 -1 0 1 -1 0 2 -1 1 -2 2 1 0 0 -2 6 1 -2 2 -1 0 -1 1 2 0 -3 1 1 0 -1 -3 -2 0 -3 -3
1 -1 0 0 1 0 0 1 0 0 0 1 0 2 -1 0 0 1 0 -1 1 -2 0 0 1 6 0 -1 -1 -1 2 1 -1 -3 -1 0 2 -2 1 0 0 1 0 -1
1 0 0 2 1 2 -2 1 -1 -1 0 0 -2 2 -2 -1 -1 0 1 0 -1 -2 1 1 -2 0 6 1 3 0 3 2 -3 0 3 -2 2 -1 3 1 -1 2 2 -1
1 0 -1 -1 1 -1 0 -2 -1 0 1 0 1 0 1 0 0 1 -2 2 0 -1 -1 -1 2 -1 1 6 1 -1 0 1 -1 1 -1 1 0 2 1 -2 -2 0 -1 1
1 -1 -1 2 0 2 -1 0 0 0 1 0 0 0 -1 1 1 0 1 0 -2 0 1 0 -1 -1 3 1 6 -1 3 0 -2 2 2 -1 1 0 1 0 -1 0 1 1
-1 0 1 0 -2 -1 -1 2 2 -3 -1 0 1 -2 2 0 1 -3 2 1 0 1 1 -1 0 -1 0 -1 -1 8 -3 -3 2 3 -1 -2 -1 2 -2 2 1 -1 0 1
1 -1 -1 2 2 3 -1 2 0 1 2 -1 -2 3 -3 -2 -1 2 0 -3 0 -1 0 0 -1 2 3 0 3 -3 8 2 -4 -3 3 0 3 -1 3 0 -1 0 3 0
3 1 0 1 2 3 0 -1 -1 -1 1 0 -2 3 -2 0 0 1 -2 1 0 -1 -2 1 1 1 2 1 0 -3 2 8 -2 0 2 1 1 -1 1 1 -1 1 1 -1
-3 1 1 0 -1 -3 1 1 2 -1 -1 2 2 -3 3 0 0 0 0 3 -2 1 1 1 2 -1 -3 -1 -2 2 -4 -2 8 1 -3 1 0 -1 -4 -1 0 -1 -3 -1
1 1 0 1 -2 1 0 -1 1 -2 -1 0 2 -3 2 3 3 -3 1 3 -3 3 1 -1 0 -3 0 1 2 3 -3 0 1 8 0 -2 -2 2 -3 1 1 0 -1 2
2 1 1 2 0 4 -1 1 -2 0 1 -1 -3 3 -3 -1 -1 0 1 -2 -1 0 0 2 -3 -1 3 -1 2 -1 3 2 -3 0 8 0 0 0 3 3 -1 0 3 1
1 1 -2 -2 1 -2 3 -1 -2 0 2 0 1 1 0 0 -1 0 -2 1 1 0 -4 0 1 0 -2 1 -1 -2 0 1 1 -2 0 8 0 -1 1 0 -2 1 -1 -1
0 -1 -2 0 3 0 0 1 2 -1 0 -1 0 0 -2 0 -2 1 0 1 -1 0 1 1 1 2 2 0 1 -1 3 1 0 -2 0 0 8 -1 1 0 0 1 1 -3
0 0 -1 -1 -1 0 0 0 0 0 2 -1 2 -2 2 0 2 0 0 1 0 2 -1 0 0 -2 -1 2 0 2 -1 -1 -1 2 0 -1 -1 8 -1 0 -1 -2 0 3
1 0 -1 0 2 0 -1 -1 -3 2 1 0 -3 3 -3 -1 -3 1 -1 -2 1 -2 -1 2 -1 1 3 1 1 -2 3 1 -4 -3 3 1 1 -1 8 -1 -2 2 2 -2
1 1 0 1 -2 2 0 2 0 -3 2 -1 1 1 0 -1 1 -2 3 -1 0 2 -1 1 -3 0 1 -2 0 2 0 1 -1 1 3 0 0 0 -1 8 1 -1 3 3
0 -3 -1 0 -1 0 0 0 3 -1 0 -1 1 -3 2 0 2 -1 0 -1 -1 2 1 -1 -2 0 -1 -2 -1 1 -1 -1 0 1 -1 -2 0 -1 -2 1 8 -1 1 1
3 0 0 -1 3 -2 1 -1 -2 2 -1 -1 0 0 -3 2 -2 -2 0 1 -1 -2 0 0 0 1 2 0 0 -1 0 1 -1 0 0 1 1 -2 2 -1 -1 8 -1 -4
1 0 -1 1 -1 3 -1 1 -1 -2 2 -1 0 3 -2 -3 0 1 1 -2 0 1 1 0 -3 0 2 -1 1 0 3 1 -3 -1 3 -1 1 0 2 3 1 -1 8 3
0 1 0 1 -4 2 1 1 -1 -3 3 1 2 0 3 -2 3 0 2 -1 -1 2 0 0 -3 -1 -1 1 1 1 0 -1 -1 2 1 -1 -3 3 -2 3 1 -4 3 10
-
DIVISORS (elementary divisors)
1^22*2^22
-
MINIMAL_NORM
6
-
PROPERTIES
INTEGRAL = 1
MODULAR = 2
-
REFERENCES
C. Bachoc, Applications of coding theory to the construction of modular lattices J. Comb. Th A 78-1 (1997) 92-119
-
NOTES
unimodular lattice over the Hurwitz order
-
LAST_LINE (required)
Haftungsausschluss/Disclaimer
Gabriele Nebe